In 1939 or 1940, Emanuel Zacchini took his human-ca act to an extreme: After bei

Question

In 1939 or 1940, Emanuel Zacchini took his human-ca act to an extreme: After being shot from a cannon, he soared over three Ferris whoels and into a net (see angle of 520 (a) Treating him as a partide, calcadlate his clearance over the firnst wheal. (b) It' he the net's center have been positioned (neglect air drag)? the figure). Assume that he is launched with a speed of 28 m/s and at an reached maximum height over the máddle wheel, by how much did he clear it? () How far from the cannon should t 5m 17m 4.5m Net 24m Units (a) Number (b) Number (c) Number

Explanation / Answer

given

yo = 4.5 m
vo = 28 m/s
theta = 52 degrees
vox = vo*cos(52) = 28*cos(52) = 17.2 m/s
voy = vo*sin(52) = 28*sin(52) = 22.1 m/s

a) time taken to reach first ferries wheel, t = x/vox

= 24/17.2

= 1.395 s

now use, y - yo = voy*t + (1/2)*ay*t^2

y - 4.5 = 22.1*1.395 + (1/2)*(-9.8)*1.395^2

y = 25.8 m

so, the peron clears the first ferries wheel by = y - h

= 25.8 - 17

= 8.8 m <<<<<<<<<<<<<------------------Answer

b) maximum height reached by the person, h_max = yo + voy^2/(2*g)

= 4.5 + 22.1^2/(2*9.8)

= 29.4 m

so, the peron clears the first ferries wheel by = h_max - yo

= 29.8 - 17

= 12.8 m <<<<<<<<<<<<<------------------Answer

c) Range = vo^2*sin(2*theta)/g

= 28^2*sin(2*52)/9.8

= 77.6 m <<<<<<<<<<<<<------------------Answer

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